% !TeX TXS-program:compile = txs:///arara
% arara: pdflatex: {shell: yes, synctex: no, interaction: batchmode}
% arara: pdflatex: {shell: yes, synctex: no, interaction: batchmode}
% arara: pdflatex: {shell: yes, synctex: no, interaction: batchmode} if found('log', '(undefined references|Please rerun|Rerun to get)')

\documentclass[11pt,a4paper]{ltxdoc}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{tkz-grapheur}
\pgfplotsset{compat=newest}
\usepackage{amsmath}
\usepackage{fancyvrb}
\usepackage{fancyhdr}
\usepackage{hyperref}
\usepackage{nicefrac}
\usepackage{fontawesome5}
\usepackage{tcolorbox}
\usepackage{minted2}
\tcbuselibrary{skins,minted}
\fancyhf{}
\renewcommand{\headrulewidth}{0pt}
\lfoot{\sffamily\small [tkz-grapheur]}
\rfoot{\sffamily\small - \thepage{} -}
\usepackage{hologo}
\providecommand\tikzlogo{Ti\textit{k}Z}
\providecommand\TeXLive{\TeX{}Live\xspace}
\providecommand\PSTricks{\textsf{PSTricks}\xspace}
\let\pstricks\PSTricks
\let\TikZ\tikzlogo

\urlstyle{same}
\hypersetup{pdfborder=0 0 0}
\usepackage[margin=2cm]{geometry}
\setlength{\parindent}{0pt}
\def\TPversion{\tkzgrapheurversion}
\def\TPdate{\tkzgrapheurdateversion}
\usepackage{soul}
\usepackage{codehigh}
\usepackage{tabularray}
\usepackage{alphalph}
\sethlcolor{lightgray!25}
\NewDocumentCommand\MontreCode{ m }{%
	\hl{\vphantom{\texttt{pf}}\texttt{#1}}%
}
\usepackage[english]{babel}

\renewcommand{\footnoterule}{\vfill\kern -3pt \hrule width 0.4\columnwidth \kern 2.6pt}

\begin{document}

\pagestyle{fancy}

\thispagestyle{empty}

\begin{center}
	\begin{minipage}{0.88\linewidth}
	\begin{tcolorbox}[colframe=yellow,colback=yellow!15]
		\begin{center}
			\begin{tabular}{c}
				{\Huge \texttt{tkz-grapheur [en]}}\\
				\\
				{\LARGE A grapher, based}\\
				\\
				{\LARGE on \textsf{\TikZ} and \textsf{xint}.}\\
				\\
				{\small \texttt{Version \TPversion{} -- \TPdate}}
		\end{tabular}
		\end{center}
	\end{tcolorbox}
\end{minipage}
\end{center}

\begin{center}
	\begin{tabular}{c}
	\texttt{Cédric Pierquet}\\
	{\ttfamily c pierquet -- at -- outlook . fr}\\
	\texttt{\url{https://github.com/cpierquet/latex-packages/tree/main/tkz-grapheur}} \\
\end{tabular}
\end{center}

\hrule

\vfill

\begin{tcolorbox}[colframe=lightgray,colback=lightgray!5,halign=center]
\begin{GraphTikz}[x=0.85cm,y=0.35cm,Xmin=0,Xmax=10,Ymin=0,Ymax=16]
	%préparation de la fenêtre
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{0,1,...,10}{0,2,...,16}
	%déf des fonctions avec nom courbe + nom fonction + expression
	\DefineCurve[Name=cf]<f>{3*x-6}
	\DefineCurve[Name=cg]<g>{-(x-6)^2+12}
	%antécédents et intersection
	\FindIntersections[Disp=false,Name=K]{cf}{cg}
	\FindCounterimage[DispLine,Color=orange,Name=I]{cg}{8}
	\FindCounterimage[Disp=false,Name=J]{cg}{0}
	%intégrale sous une courbe, avec intersection
	\DrawIntegral%
	[Colors=blue/purple,Bounds=nodes,Style=hatch,Hatch=bricks]%
		{g(x)}%
		{(I-2)}{(J-2)}
	%intégrale entre les deux courbes
	\DrawIntegral[Bounds=nodes,Type=fct/fct]{f(x)}[g(x)]{(K-1)}{(K-2)}
	%tracé des courbes et des points
	\DrawCurve[Color=red]{f(x)}
	\DrawCurve[Color=teal]{g(x)}
	\MarkPts<\small>{(K-1)/below right/L,(K-2)/above left/M}%
	\MarkPts[violet]<\small>{(I-1)/above left/D,(I-2)/above right/E}%
	%essai de tangente
	\DrawTangent[Colors=pink!75!black/yellow,OffsetL=2,OffsetR=2,DispPt]{g}{5}
	%essai d'image
	\DrawRanges[Colors=cyan]{g}{7,7.25,7.5}
	%surimpression des axes
	\DrawAxisGrids[Grads=false,Grid=false,Enlarge=2.5mm]{0,1,...,10}{0,2,...,16}
\end{GraphTikz}
\end{tcolorbox}

\vspace*{5mm}

\begin{tcolorbox}[colframe=lightgray,colback=lightgray!5,halign=center]
\begin{GraphTikz}%
	[x=3.5cm,y=4cm,
	Xmin=0,Xmax=3.5,Xgrid=pi/12,Xgrids=pi/24,
	Ymin=-1.05,Ymax=1.05,Ygrid=0.2,Ygrids=0.05]
	%préparation de la fenêtre
	\DrawAxisGrids[Grads=false,Enlarge=2.5mm,Format=ntrig/nsqrt]%
	{pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi}
	{0,sqrt(2)/2,1/2,sqrt(3)/2,1,-1,-sqrt(3)/2,-1/2,-sqrt(2)/2}
	%rajouter des valeurs
	\AddXvalues{0.25,1.4,3.3}{0.25,1.4,3.3}
	%fonction trigo (déf + tracé)
	\DefineCurve[Name=ccos,Start=0,End=pi]<fcos>{cos(x)}
	\DefineCurve[Name=csin,Start=0,End=pi]<fsin>{sin(x)}
	%intégrale
	\FindIntersections[Disp=false,Name=JKL]{ccos}{csin}
	%\DefinirPts{FIN/pi/0}
	\DrawIntegral%
	[Bounds=node/abs,Type=fct/fct,Colors=cyan/cyan!50]%
		{fsin(x)}[fcos(x)]%
		{(JKL-1)}{pi}
	%tracé des courbes
	\DrawCurve[Color=red,Start=0,End=pi]{fcos(x)}
	\DrawCurve[Color=olive,Start=0,End=pi]{fsin(x)}
	%antécédent(s)
	\DrawCounterimage[Color=blue/teal!50!black,Lines]{ccos}{-0.25}
	\DrawCounterimage[Colors=red/magenta!50!black,Lines]{csin}{0.5}
	\DrawCounterimage[Colors=orange/orange!50!black,Lines]{csin}{sqrt(2)/2}
	\DrawCounterimage[Colors=green!50!black/green,Lines]{csin}{sqrt(3)/2}
	%surimpression axes
	\DrawAxisGrids[Grid=false,Enlarge=2.5mm,Format=ntrig/nsqrt]%
	{pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi}
	{0,sqrt(2)/2,1/2,sqrt(3)/2,1,-1,-sqrt(3)/2,-1/2,-sqrt(2)/2}
\end{GraphTikz}
\end{tcolorbox}

\vfill

\hfill{\footnotesize\textit{\ttfamily To my Dad.}}

\vspace*{5mm}

\pagebreak

\phantomsection

\hypertarget{matoc}{}

\tableofcontents

\vspace*{5mm}

\hrule

\vspace*{5mm}

\pagebreak

\section{Introduction}

\subsection{Description and general ideas}

With this modest package, far from the capabilities offered by the excellent packages \MontreCode{tkz-*}\footnote{for example tkz-base \url{https://ctan.org/pkg/tkz-base} and tkz- fct \url{https://ctan.org/pkg/tkz-fct}.} (by Alain Matthes) or \MontreCode{tzplot}\footnote{CTAN: \url{https://ctan.org/pkg/ tzplot}.} (by In-Sung Cho), it is possible to work on function graphs, in \TikZ\ language, in an \textit{intuitive} and \textit{explicit} way.

\smallskip

Concerning the overall operation:

\smallskip

\begin{itemize}
	\item particular styles for the objects used have been defined, but they can be modified locally;
	\item the name of the commands is in \textit{operational} form, so that the construction of the graphic elements has an almost \textit{algorithmic} form.
\end{itemize}

\subsection{Overall operation}

To schematize, it \textit{is enough}:

\smallskip

\begin{itemize}
	\item to declare the parameters of the graphics window (\textbf{units in cm !});
	\item to display grid/axes/graduations;
	\item to declare functions or interpolation curves;
	\item to possibly declare particular points;
	\item to place a point scatter.
\end{itemize}

\smallskip

It will then be possible:

\begin{itemize}
	\item to draw curves;
	\item to graphically determine images or backgrounds;
	\item to add elements of derivation (tangents) or integration (domain);
	\item to draw a linear fit line or the curve of another fit.
\end{itemize}

\subsection{Packages used, and package options}

The package uses:

\smallskip

\begin{itemize}
	\item \MontreCode{tikz}, with the libraries \MontreCode{calc,intersections,patterns,patterns.meta,bbox};
	\item \MontreCode{simplekv}, \MontreCode{xintexpr}, \MontreCode{xstring}, \MontreCode{listofitems};
	\item \MontreCode{xint-regression}\footnote{CTAN: \url{https://ctan.org/pkg/xint-regression}.} (for regressions, switchable via \MontreCode{[noxintreg]}).
\end{itemize}

\smallskip

The package also loads \MontreCode{siunitx} with the classic options, but it is possible not to load it using the \MontreCode{[nosiunitx]} option.

\smallskip

The package also loads the \TikZ\ \MontreCode{babel} library, but it is possible not to load it using the \MontreCode{[notikzbabel]} option.

\smallskip

The different options are obviously cumulative.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%loading by default, with french setup of siunitx
\usepackage{tkz-grapheur}
%loading by default, with normal setup of siunitx
\usepackage[english]{tkz-grapheur}

%loading without sinuitx, to be loaded manually
\usepackage[nosiunitx]{tkz-grapheur}

%loading without tikz.babel
\usepackage[notikzbabel]{tkz-grapheur}
\end{tcblisting}

Also note that certain commands can use packages like \MontreCode{nicefrac}, which will therefore have to be loaded if necessary.

\smallskip

Concerning the \textit{calculations} and \textit{plots} part, the \MontreCode{xint} package takes care of it.

\subsection{Warnings}

It is possible, due to the (multiple) calculations carried out internally, that the compilation time may be a little \textit{long}.

\smallskip

The precision of the (determination) results seems to be around $10^{-4}$, which should normally guarantee \textit{satisfactory} plots and readings. It is still advisable to be cautious about the results obtained and those expected.

\subsection{Introductory example}

For example, we can start from the following example to \textit{illustrate} the flow of the commands for this package. The commands and syntax will be detailed in the following sections!

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\begin{GraphTikz}%
	[x=7.5cm,y=7.5cm,Xmin=0,Xmax=1.001,Xgrid=0.1,Xgrids=0.02,
	Ymin=0,Ymax=1.001,Ygrid=0.1,Ygrids=0.02]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]%
		{0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}
		{0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}
	\DefineCurve[Name=cf,Start=0,End=1]<f>{x*exp(x-1)}
	\DefineCurve[Name=delta,Start=0,End=1]<D>{x}
	\DrawIntegral[Type=fct/fct]{f(x)}[D(x)]{0}{1}
	\DrawCurve[Color=red]{f(x)}
	\DrawCurve[Color=teal]{D(x)}
	\DrawRanges[Colors=blue/cyan,Lines]{f}{0.8,0.9}
	\DrawCounterimage[Colors=green!50!black/olive,Lines]{cf}{0.5}
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,text only}
	\begin{GraphTikz}%
		[x=7.5cm,y=7.5cm,Xmin=0,Xmax=1.001,Xgrid=0.1,Xgrids=0.02,
		Ymin=0,Ymax=1.001,Ygrid=0.1,Ygrids=0.02]
		\DrawAxisGrids[Enlarge=2.5mm,Font=\small]%
		{0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}
		{0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}
		\DefineCurve[Name=cf,Start=0,End=1]<f>{x*exp(x-1)}
		\DefineCurve[Name=delta,Start=0,End=1]<D>{x}
		\DrawIntegral[Type=fct/fct]{f(x)}[D(x)]{0}{1}
		\DrawCurve[Color=red]{f(x)}
		\DrawCurve[Color=teal]{D(x)}
		\DrawRanges[Colors=blue/cyan,Lines]{f}{0.8,0.9}
		\DrawCounterimage[Colors=green!50!black/olive,Lines]{cf}{0.5}
	\end{GraphTikz}
\end{tcblisting}

\newpage

\section{Basic Styles and Environment Creation}

\subsection{Basic Styles}

The styles used for plots are given below.

\smallskip

For \textit{simplicity} purposes, only the color of the elements can be configured, but if the user wishes, he can redefine the proposed styles.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%parameters declared and stored (usable in the environment a posteriori)
\tikzset{
	Xmin/.store in=\pflxmin,Xmin/.default=-3,Xmin=-3,
	Xmax/.store in=\pflxmax,Xmax/.default=3,Xmax=3,
	Ymin/.store in=\pflymin,Ymin/.default=-3,Ymin=-3,
	Ymax/.store in=\pflymax,Ymax/.default=3,Ymax=3,
	Origx/.store in=\pflOx,Origx/.default=0,Origx=0,
	Origy/.store in=\pflOy,Origy/.default=0,Origy=0,
	Xgrid/.store in=\pflgrillex,Xgrid/.default=1,Xgrid=1,
	Xgrids/.store in=\pflgrillexs,Xgrids/.default=0.5,Xgrids=0.5,
	Ygrid/.store in=\pflgrilley,Ygrid/.default=1,Ygrid=1,
	Ygrids/.store in=\pflgrilleys,Ygrids/.default=0.5,Ygrids=0.5
}
\end{tcblisting}

We therefore find:

\smallskip

\begin{itemize}
	\item the origin of the mark (\MontreCode{Origx}/\MontreCode{Origy});
	\item the extreme values of the axes (\MontreCode{Xmin}/\MontreCode{Xmax}/\MontreCode{Ymin}/\MontreCode{Ymax});
	\item the parameters of the main and secondary grids (\MontreCode{Xgrid}/\MontreCode{Xgrids}/\MontreCode{Ygrid}/\MontreCode{Ygrids}).
\end{itemize}

\smallskip

Concerning the styles of \textit{objects}, they are given below.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\tikzset{tkzgrphnode/.style={}}
\tikzset{tkzgrphpoint/.style={line width=0.95pt}}
\tikzset{tkzgrphpointc/.style={radius=1.75pt}}
\tikzset{tkzgrphscatter/.style={radius=1.75pt}}
\tikzset{tkzgrphframe/.style={line width=0.8pt,gray}}
\tikzset{tkzgrphcurve/.style={line width=1.05pt}}
\tikzset{tkzgrphline/.style={line width=0.8pt}}
\tikzset{tkzgrpharrowl/.style={<-,>=latex}}
\tikzset{tkzgrpharrowr/.style={->,>=latex}}
\tikzset{tkzgrpharrowlr/.style={<->,>=latex}}
\tikzset{tkzgrphcounterimage/.style={line width=0.9pt,densely dashed}}
\tikzset{tkzgrphrange/.style={line width=0.9pt,densely dashed,->,>=latex}}
\tikzset{tkzgrphgridp/.style={thin,lightgray}}
\tikzset{tkzgrphgrids/.style={very thin,lightgray}}
\tikzset{tkzgrphaxes/.style={line width=0.8pt,->,>=latex}}
\end{tcblisting}

The idea is therefore to be able to redefine styles globally or locally, and possibly add elements, using \mintinline{latex}|mystyle/.append style={...}|.

\subsection{Creating the environment}\label{creaenvt}

\subsubsection{Manual values}

The proposed environment is based on \TikZ, so that any \textit{classic} command linked to \TikZ\ can be used alongside the package commands!

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\begin{GraphTikz}[tikz options]<keys>
	%code(s)
\end{GraphTikz}
\end{tcblisting}

The \MontreCode{[tikz options]} are the \textit{classic} options that can be passed to a \TikZ\ environment, as well as the \textsf{axes/grids/window} keys presented previously.

\smallskip

The specific (and optional) \MontreCode{<keys>} are:

\smallskip

\begin{itemize}
	\item \MontreCode{ThickGrad}: size of the axis graduations (\MontreCode{3pt} for 3pt \textit{above} and 3pt \textit{below});
	\item \MontreCode{Frame}: boolean (\MontreCode{false} by default) to display a frame which delimits the graphic window (excluding possible graduations).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}
	[x=0.075cm,y=0.03cm,Xmin=0,Xmax=160,Xgrid=20,Xgrids=10,
	Origy=250,Ymin=250,Ymax=400,Ygrid=25,Ygrids=5]
	<Frame>
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	<Frame>
\end{GraphTikz}
\end{tcblisting}

It will obviously be more meaningful with the added graphic elements!

\subsubsection{With choice of dimensions}

It is also possible (currently being tested) to specify the dimensions of the graph, letting the code determine the correct units.

In this case, the keys and arguments differ slightly, notably via the key \MontreCode{<Size=width/height>}:

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%fixed dimensions (excluding graduations)
\begin{GraphTikz}%
	[Xgrid=10,Xgrids=5,Ygrid=50,Ygrids=25]
	%Xgrid(s) and/or Ygrid(s) in this case
	<Xmin=0,Xmax=100,Ymin=0,Ymax=250,Size={10cm/5cm}>
	\DrawAxisGrids[]{auto}{auto}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Grids and axes}\label{creaaxesgr}

The first command \textit{useful} will allow you to create the grids, axes and graduations.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawAxisGrids[keys]{gradX}{gradY}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Grid}: boolean (\MontreCode{true} by default) to display the grids (for a single grid, simply set the identical parameters for \MontreCode{Xgrid}/\MontreCode{Xgrids} or \MontreCode {Ygrid}/\MontreCode{Ygrids});
	\item \MontreCode{Enlarge}: addition at the end of the axes (\MontreCode{0} by default);
	\item \MontreCode{Grads}: boolean (\MontreCode{true} by default) for graduations;
	\item \MontreCode{Font}: global font for graduations {\MontreCode{empty} by default};
	\item \MontreCode{Format}: special formatting (see below) of the axis values.
\end{itemize}

\smallskip

Concerning the \MontreCode{Format} key, it allows you to specify a specific setting for the axis values.

\smallskip

It can be given in the form \MontreCode{fmt} for combined formatting, or in the form \MontreCode{fmtX/fmtY} to differentiate the formatting.

\smallskip

The possible options are:

\smallskip

\begin{itemize}
	\item \MontreCode{num}: format with \textsf{siunitx};
	\item \MontreCode{year}: format in year;
	\item \MontreCode{frac}: format as fraction \textsf{frac};
	\item \MontreCode{dfrac}: format as fraction \textsf{dfrac};
	\item \MontreCode{nfrac}: format as fraction \textsf{nicefrac};\hfill (to load!)
	\item \MontreCode{trig}: format in trig with \textsf{frac};
	\item \MontreCode{dtrig}: format in trig with \textsf{dfrac};
	\item \MontreCode{ntrig}: format in trig with \textsf{nfrac};
	\item \MontreCode{sqrt}: format in root with \textsf{frac};
	\item \MontreCode{dsqrt}: format in root with \textsf{dfrac};
	\item \MontreCode{nsqrt}: format in root with \textsf{nicefrac}.
\end{itemize}

\smallskip

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}
	[x=0.075cm,y=0.03cm,Xmin=0,Xmax=160,Xgrid=20,Xgrids=10,
	Origy=250,Ymin=250,Ymax=400,Ygrid=25,Ygrids=5]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{0,10,...,160}{250,275,...,400}
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
\end{GraphTikz}
\end{tcblisting}

Note that there are the Boolean keys \MontreCode{[Behind]} (without the graduations) and \MontreCode{[Above]} (without the grid) to display the axes in \textit{under/over}-printing mode in the case of integrals for example.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=2.75cm,y=3cm,
	Xmin=0,Xmax=3.5,Xgrid=pi/12,Xgrids=pi/24,
	Ymin=-1.05,Ymax=1.05,Ygrid=0.2,Ygrids=0.05]
	\DrawAxisGrids[Enlarge=2.5mm,Format=dtrig/nsqrt,Font=\footnotesize]%
	{pi/6,pi/4,pi/3,pi/2,2*pi/3,3*pi/4,5*pi/6,pi}
	{0,sqrt(2)/2,1/2,sqrt(3)/2,1,-1,-sqrt(3)/2,-1/2,-sqrt(2)/2}
\end{GraphTikz}
\end{tcblisting}

In the case where the formatting does not give satisfactory result(s), it is possible to use a generic command for placing the graduations.

\subsection{Adding values manually}\label{additionvals}

It is also possible to use a specific command to place values on the axes, independently of an \textit{automated} formatting system.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
in the environment
\AddXvalues[keys]{grads}{formatted values}
\AddYvalues[keys]{grads}{formatted values}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Font}: global font for graduations {\MontreCode{empty} by default};
	\item \MontreCode{Lines}: boolean to add the tick marks {\MontreCode{true} by default}.
\end{itemize}

\smallskip

The mandatory arguments correspond to the x-coordinates (in \TikZ\ language) and to the labels (in \LaTeX\ language) of the graduations.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=2.75cm,y=3cm,
	Xmin=0,Xmax=3.5,Xgrid=pi/12,Xgrids=pi/24,
	Ymin=-1.05,Ymax=1.05,Ygrid=0.2,Ygrids=0.05]
	\DrawAxisGrids[Grads=false,Enlarge=2.5mm]{}{}
	\AddXvalues
		{0.15,0.6,pi/2,2.8284}
		{\num{0.15},$\frac35$,$\displaystyle\frac{\pi}{2}$,$\sqrt{8}$}
	\AddYvalues
		{-1,0.175,0.3,sqrt(3)/2}
		{\num{-1},\num{0.175},$\nicefrac{3}{10}$,$\frac{\sqrt{3}}{2}$}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Nodes for window or axis}

Alongside the creation of the window (and possibly the axes), nodes are created for later reuse (e.g., text placement).

\begin{itemize}
	\item 9 \textcolor{red}{nodes} for window:
	\begin{itemize}
		\item \MontreCode{(graph-nw)}, \MontreCode{(graph-n)}, \MontreCode{(graph-ne)} ;
		\item \MontreCode{(graph-w)}, \MontreCode{(graph-c)}, \MontreCode{(graph-e)} ;
		\item \MontreCode{(graph-sw)}, \MontreCode{(graph-s)}, \MontreCode{(graph-se)} ;
	\end{itemize}
	\item 4 \textcolor{blue}{nodes} for axis:
	\begin{itemize}
		\item \MontreCode{(xaxis-w)}, \MontreCode{(xaxis-e)} ;
		\item \MontreCode{(yaxis-s)}, \MontreCode{(yaxis-n)} ;
	\end{itemize}
	\item 1 \textcolor{violet}{node} for origin:
	\begin{itemize}
		\item \MontreCode{(axis-orig)} ;
	\end{itemize}
	\item 2 \textcolor{purple}{nodes} for \textit{enlarge} axis:
	\begin{itemize}
		\item \MontreCode{(xaxis-ee)} ;
		\item \MontreCode{(yaxis-nn)}.
	\end{itemize}
\end{itemize}

\begin{center}%démo !!
	\begin{GraphTikz}[Xmin=-7,Xmax=4,Ymin=-3,Ymax=5,Xgrids=0.5,Ygrids=0.5]
		\tikzset{labellegende/.style={outer sep=2.25pt,inner sep=0.75pt,font=\scriptsize\ttfamily,fill=white}}
		\DrawAxisGrids[Enlarge=5mm]{}{}
		%nœuds (v0.30a)
		\draw[red,fill=yellow] (graph-nw) circle[radius=2pt] node[above left,labellegende] {nw} ;
		\draw[red,fill=yellow] (graph-n) circle[radius=2pt] node[above,labellegende] {n} ;
		\draw[red,fill=yellow] (graph-ne) circle[radius=2pt] node[above right,labellegende] {ne} ;
		\draw[red,fill=yellow] (graph-e) circle[radius=2pt] node[right,labellegende] {e} ;
		\draw[red,fill=yellow] (graph-se) circle[radius=2pt] node[below right,labellegende] {se} ;
		\draw[red,fill=yellow] (graph-s) circle[radius=2pt] node[below,labellegende] {s} ;
		\draw[red,fill=yellow] (graph-sw) circle[radius=2pt] node[below left,labellegende] {sw} ;
		\draw[red,fill=yellow] (graph-w) circle[radius=2pt] node[left,labellegende] {w} ;
		\draw[red,fill=yellow] (graph-c) circle[radius=2pt] node[above,labellegende] {c} ;
		\draw[blue,fill=orange] (xaxis-w) circle[radius=2pt] node[left,labellegende] {w} ;
		\draw[blue,fill=orange] (xaxis-e) circle[radius=2pt] node[above,labellegende] {e} ;
		\draw[blue,fill=orange] (yaxis-s) circle[radius=2pt] node[below,labellegende] {w} ;
		\draw[blue,fill=orange] (yaxis-n) circle[radius=2pt] node[right,labellegende] {n} ;
		\draw[violet,fill=teal] (axis-orig) circle[radius=2pt] node[above right,labellegende] {orig} ;
		\draw[purple,fill=gray] (xaxis-ee) circle[radius=2pt] node[right,labellegende] {ee} ;
		\draw[purple,fill=gray] (yaxis-nn) circle[radius=2pt] node[above,labellegende] {nn} ;
	\end{GraphTikz}
\end{center}

\pagebreak

\section{Specific definition commands}

\subsection{Draw a line}\label{tracstraight}

The idea is to propose a command to draw a line (or an asymptote), from:

\begin{itemize}
	\item of two points (or nodes);
	\item of a point (or node) and the slope.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawLine[keys]{point or node}{point or node or slope}
\DrawAsymptote[keys]{x value}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: possible name of the plot (for reuse);
	\item \MontreCode{Slope}: boolean to specify that the slope is used (\MontreCode{false} by default);
	\item \MontreCode{Start}: start of the plot (\MontreCode{\textbackslash pflxmin} by default);
	\item \MontreCode{End}: end of the plot (\MontreCode{\textbackslash pflxmax} by default);
	\item \MontreCode{Color}: color of the trace (\MontreCode{black} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\DefinePts[Mark,Color=gray]{A/-4/3,B/2/0,C/0/-1}
	\DrawLine[Color=red]{(-2,-1)}{(2,4)}
	\DrawLine[Color=blue,Start=-5,End=3]{(A)}{(B)}
	\DrawLine[Color=olive,Slope]{(C)}{0.25}
	\DrawAsymptote[Color=brown]{-6}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Define a function, draw the curve of a function}\label{deftracfct}

The idea is to define a function, for later reuse. This command \textit{creates} the function, without tracing it, because in certain cases elements will have to be traced beforehand.

\smallskip

There is also a command to plot the curve of a previously defined function.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DefineCurve[keys]<fct name>{xint formula}
\DrawCurve[keys]{xint formula}
\end{tcblisting}

The optional \MontreCode{[keys]} for definition or tracing are:

\smallskip

\begin{itemize}
	\item \MontreCode{Start}: lower bound of the definition set (\MontreCode{\textbackslash pflxmin} by default);
	\item \MontreCode{End}: lower bound of the definition set (\MontreCode{\textbackslash pflxmax} by default);
	\item \MontreCode{Name}: name of the curve (important for the rest!);
	\item \MontreCode{Color}: color of the trace (\MontreCode{black} by default);
	\item \MontreCode{Step}: plot step (it is determined \textit{automatically} at the start but can be modified);
	\item \MontreCode{Trace}: boolean to also trace the curve (\MontreCode{false} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	%definition of the function + drawing of the curve
	\DefineCurve[Name=cf,Start=5,End=19]<f>{-2*x+3+24*log(2*x)}
	\DrawCurve[Color=red,Start=5,End=19]{f(x)}
	%or in a single command if "sufficient"
	%\DefineCurve[Name=cf,Start=5,End=19,Trace]<f>{-2*x+3+24*log(2*x)}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Define/draw an interpolation curve (simple)}\label{deftracinterpo}

It is also possible to define a curve via support points, therefore a simple interpolation curve.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DefineInterpoCurve[keys]{list of support points}
\DrawInterpoCurve[keys]{list of support points}
\end{tcblisting}

The optional \MontreCode{[keys]} for definition or tracing are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: name of the interpolation curve (important for the rest!);
	\item \MontreCode{Color}: color of the trace (\MontreCode{black} by default);
	\item \MontreCode{Tension}: setting the \textit{tension} of the interpolation plot (\MontreCode{0.5} by default);
	\item \MontreCode{Trace}: boolean to also trace the curve (\MontreCode{false} by default).
\end{itemize}

The mandatory argument allows you to specify the list of support points in the form \MontreCode{(x1,y1)(x2,y2)...}.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5]
	\DrawAxisGrids[Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5}
	%simple interpolation curves (with diff tension)
	\DefineInterpoCurve[Name=interpotest,Color=blue,Trace]%
		{(-6,4)(-2,-2)(3,3.5)}
	\DefineInterpoCurve[Name=interpotest,Color=red,Trace,Tension=1]%
		{(-6,4)(-2,-2)(3,3.5)}
\end{GraphTikz}
\end{tcblisting}

\newpage

\subsection{Define/draw an interpolation curve (Hermite)}\label{deftracfctspline}

It is also possible to define a curve via support points, therefore an interpolation curve with derivative control.

\smallskip

Some operations require different techniques depending on the type of function used, a \textsf{Boolean} key \MontreCode{Spline} will allow the code to adapt its calculations depending on the object used.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DefineSplineCurve[keys]{list of support points}[\macronomspline]
\DrawSplineCurve[keys]{list of support points}[\macronomspline]
\end{tcblisting}

The optional \MontreCode{[keys]} for definition or tracing are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: name of the interpolation curve (important for the rest!);
	\item \MontreCode{Coeffs}: modify (see the \textsf{ProfLycee}\footnote{CTAN documentation: \url{https://ctan.org/pkg/proflycee}} the \textit{coefficients} of the spline;
	\item \MontreCode{Color}: color of the trace (\MontreCode{black} by default);
	\item \MontreCode{Trace}: boolean to also trace the curve (\MontreCode{false} by default).
\end{itemize}

The mandatory argument allows you to specify the list of support points in the form \MontreCode{x1/y1/f'1§x2/y2/f'2§...} with:

\begin{itemize}
	\item \MontreCode{xi/yi} the coordinates of the point;
	\item \MontreCode{f'i} the derivative at the support point.
\end{itemize}

\smallskip

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5]
	\DrawAxisGrids[Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5}
	%definition of the list of spline support points
	\def\LISTETEST{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}
	%definition and plot of the cubic spline
	\DefineSplineCurve[Name=splinetest,Trace,Color=olive]{\LISTETEST}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Define points as nodes}\label{defpts}

The second idea is to work with \TikZ nodes, which could be useful for tangent plots, representations of integrals$\ldots$

\smallskip

It is also possible to define nodes for \textit{image} points.

\smallskip

Certain commands (explained later) allow you to determine particular points of curves in the form of nodes, so it seems interesting to be able to define them directly.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%by coordinates
\DefinePts[keys]{Name1/x1/y1,Name2/x2/y2,...}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Mark}: boolean to mark points (\MontreCode{false} by default);
	\item \MontreCode{Color}: color of the points, if \MontreCode{Mark=true} (\MontreCode{black} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%as image
\DefineRange[keys]{object}{abscissa}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: node name (\MontreCode{empty} by default);
	\item \MontreCode{Spline}: boolean to specify that a spline is used (\MontreCode{false} by default).
\end{itemize}

The first mandatory argument is the \textit{object} considered (name of the curve for the spline, function otherwise); the second is the abscissa of the point considered.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	%definition of the function + drawing of the curve
	\DefineFunction[Name=cf,Start=5,End=19,Trace,Color=red]<f>{-2*x+3+24*log(2*x)}
	%manual nodes
	\DefinePts[Mark,Color=brown]{A/7/42,B/16/49}
	%imagenode
	\DefineRange[Name=IMGf]{f}{14}
	\MarkPts*[Style=x,Color=blue]{(IMGf)} %see next section;-)
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Mark Points}\label{markpts}

The idea is to offer something to score points with a particular style.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\MarkPts(*)[keys]<font>{list}
\end{tcblisting}

The \textit{starred} version scores the points without the \textit{names}, while the \textit{unstarred} version displays them:

\begin{itemize}
	\item in the case of the \textit{starred} version, the list should be given in the form \MontreCode{(ptA),(ptB),...};
	\item otherwise, the list should be given in the form \MontreCode{(ptA)/poslabelA/labelA,...}.
\end{itemize}

\smallskip

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Color}: color (\MontreCode{black} by default);
	\item \MontreCode{Style}: style of marks (\MontreCode{o} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=1.5cm,y=1.5cm,Ymin=-2]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\DefinePts{A/1.75,-1.25}\MarkPts[Color=pink]{(A)/below/A} %round (default)
	\MarkPts[Color=teal]{(1,1)/below/M}
	\MarkPts[Color=red,Style=x]{(1.25,1)/below/$A$} %cross
	\MarkPts[Color=orange,Style=+]<\small\sffamily>{(1.5,1)/below/K} %plus
	\MarkPts[Color=blue,Style=c]{(1.75,1)/below/P} %square
	\MarkPts[Color=gray,Style=d]{(2,1)/below/P} %diamond
	\MarkPts*[Color=orange/yellow]{(2,2),(2.5,2.25)} %two-tone round
	\MarkPts*[Style=+,Color=red]{(1,2)}
	\MarkPts*[Style=x,Color=blue]{(2.25,1)}
	\MarkPts*[Style=c,Color=magenta]{(-2,-1)}
	\MarkPts[Color=red,Style=x]{(-1,1)/below/$A$,(-2,2)/below left/$B$}
\end{GraphTikz}
\end{tcblisting}

Note that it is also possible to modify the size of the \MontreCode{o/x/+/c} marks via the \MontreCode{[keys]}:

\begin{itemize}
	\item \MontreCode{Sizex=...} (\MontreCode{2pt} by default) for points \textit{cross};
	\item \MontreCode{Sizeo=...} (\MontreCode{1.75pt} by default) for the points \textit{circle};
	\item \MontreCode{Sizec=...} (\MontreCode{2pt} by default) for the \textit{square} points.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=1cm,y=1cm,Xmin=0,Ymin=0]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\MarkPts[Color=red,Style=x,Size=3.5pt]{(1.25,1.25)/below/$A$}
	\MarkPts[Color=teal,Size=2.5pt]{(2,2)/right/$A$}
	\MarkPts*[Color=orange,Style=c,Size=4pt]{(0.5,2.5)}
\end{GraphTikz}
\end{tcblisting}

\subsection{Retrieve node coordinates}\label{recupcoordo}

It is also possible, with a view to reusing coordinates, to recover the coordinates of a node (defined or determined).

\smallskip

The calculations are carried out by floating according to the (re)calculated units, the values are therefore approximated !

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\GetXcoord{node}[\macrox]
\GetYcoord{node}[\macroy]
\GetXYcoord{node}[\macrox][\macroy]
\end{tcblisting}

\subsection{Place text}\label{placetxt}

Note that a text placement command is available.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawTxt[keys]{(node or coordinates)}{text}
\end{tcblisting}

The available \MontreCode{[keys]} are:

\begin{itemize}
	\item \MontreCode{Font=...} (\MontreCode{\textbackslash normalsize\textbackslash normalfont} by default) for the font;
	\item \MontreCode{Color=...} (\MontreCode{black} by default) for the color;
	\item \MontreCode{Position=...} (\MontreCode{empty} by default) for the position of the text relative to the coordinates.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=1cm,y=1cm,Xmin=0,Xmax=5,Ymin=0,Ymax=1]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\DrawTxt[Color=red,Font=\LARGE,Position=right]{(1.5,0.5)}{curve $C_1$}
\end{GraphTikz}
\end{tcblisting}

\section{Specific commands for using curves}

\subsection{Image placement}\label{images}

It is possible to place points (images) on a curve, with possible construction lines.

The function/curve used must have been declared previously for this command to work.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawRanges[keys]{function or curve}{list of abscissa}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Lines}: boolean to display construction traits (\MontreCode{false} by default);
	\item \MontreCode{Colors}: color of the points/lines, in the form \MontreCode{Couleurs} or \MontreCode{ColPoint/ColLines};
	\item \MontreCode{Spline}: boolean to specify that the curve used is defined as a \textsf{spline} (\MontreCode{false} by default).
\end{itemize}

\smallskip

The first mandatory argument allows you to specify:

\smallskip

\begin{itemize}
	\item the name of the curve in the case \MontreCode{Spline=true};
	\item the name of the function otherwise.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	%definition of the function + drawing of the curve
	\DefineCurve[Name=cf,Start=5,End=19,Trace,Color=red]<f>{-2*x+3+24*log(2*x)}
	%images
	\DrawRanges[Lines,Colors=teal/blue]{f}{6,7,8,9,10}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Antecedent determination}\label{defanteced}

It is possible to graphically determine the antecedents of a given reality.

The function/curve used must have been declared previously for this command to work.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\FindCounterimage[keys]{curve}{k}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: base of the name of the \textbf{nodes} intersection (\MontreCode{S} by default, which will give \textsf{S-1}, \textsf{S-2}, etc);
	\item \MontreCode{Disp}: boolean to display the points (\MontreCode{true} by default);
	\item \MontreCode{Color}: color of the points (\MontreCode{black} by default);
	\item \MontreCode{DispLine}: boolean to display the horizontal line (\MontreCode{false} by default).
\end{itemize}

\smallskip

The first mandatory argument allows you to specify the \textbf{name} of the curve.

\smallskip

The second mandatory argument allows you to specify the value to reach.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	%definition of the function + drawing of the curve
	\DefineCurve[Name=cf,Start=5,End=19,Trace,Color=red]<f>{-2*x+3+24*log(2*x)}
	%history
	\FindCounterimage[Color=teal,DispLine,Disp]{cf}{53}
	%the two antecedents are at nodes (S-1) and (S-2)
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Antecedent construction}\label{tracanteced}

It is possible to graphically construct the antecedents.

The function/curve used must have been declared previously for this command to work.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawCounterimage[keys]{curve}{k}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Colors}: color of the points/lines, in the form \MontreCode{Color} or \MontreCode{ColPoint/ColLines};
	\item \MontreCode{Name}: name \textit{possible} for the intersection points linked to the antecedents (\MontreCode{empty} by default);
	\item \MontreCode{Lines}: boolean to display construction traits (\MontreCode{false} by default).
\end{itemize}

\smallskip

The first mandatory argument allows you to specify the \textbf{name} of the curve.

\smallskip

The second mandatory argument allows you to specify the value to reach.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	%definition of the function + drawing of the curve
	\DefineCurve[Name=cf,Start=5,End=19,Trace,Color=red]<f>{-2*x+3+24*log(2*x)}
	%history
	\DrawCounterimage[Colors=teal/cyan,Lines,Name=PO]{cf}{53}
	\GetXcoord{(PO-1)}[\premsol]
	\GetXcoord{(PO-2)}[\deuxsol]
\end{GraphTikz}

Graphically, the antecedents of 53 are (approximately):

\begin{itemize}
	\item \num{\premsol}
	\item \num{\deuxsol}
\end{itemize}
\end{tcblisting}

\pagebreak

\subsection{Intersections of two curves}\label{intersect}

It is also possible to determine (in the form of nodes) the possible points of intersection of two previously defined curves.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\FindIntersections[keys]{curve1}{curve2}
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Name}: base of the name of the \textbf{nodes} intersection (\MontreCode{S} by default, which will give \textsf{S-1}, \textsf{S-2}, etc);
	\item \MontreCode{Disp}: boolean to display the points (\MontreCode{true} by default);
	\item \MontreCode{Color}: color of the points (\MontreCode{black} by default).
\end{itemize}

\smallskip

The first mandatory argument allows you to specify the \textbf{name} of the first curve.

\smallskip

The first mandatory argument allows you to specify the \textbf{name} of the second curve.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	\DefineCurve[Name=cf,Start=5,End=19,Trace,Color=red]<f>{-2*x+3+24*log(2*x)}
	\DefineCurve[Name=cg,Start=5,End=19,Trace,Color=blue]<g>{0.25*(x-12)^2+46}
	%intersections, named (TT-1) and (TT-2)
	\FindIntersections[Name=TT,Color=darkgray,Display,Lines]{cf}{cg}
	%recovery of intersection points
	\GetXYcoord{(TT-1)}[\alphaA][\betaA]
	\GetXYcoord{(TT-2)}[\alphaB][\betaB]
\end{GraphTikz}\\
The solutions of $f(x)=g(x)$ are $\alpha \approx \num{\alphaA}$ and
$\beta \approx \num{\alphaB}$.\\
The points of intersection of the curves of $f$ and $g$ are therefore
$(\RoundNb[2]{\alphaA};\RoundNb[2]{\betaA})$ and
$(\RoundNb[2]{\alphaB};\RoundNb[2]{\betaB})$.
\end{tcblisting}

\pagebreak

\subsection{Extrema}\label{maximum}\label{minimum}

The idea (still \textit{experimental}) is to offer commands to extract the extrema of a curve defined by the package.

The command creates the corresponding node, and it is therefore possible to retrieve its coordinates for later use.

\smallskip

It is possible, by specifying it, to work on the different curves managed by the package (function, interpolation, spline).

For singular curves, it is possible that the results are not quite those expected\ldots

\smallskip

{\small\faBomb} For the moment, the \textit{limitations} are:

\begin{itemize}
	\item no management of multiple extrema (only the first will be processed)\ldots
	\item no management of extrema at the boundaries of the route\ldots
	\item no automatic recovery of curve definition parameters\ldots
	\item compilation time may be longer\ldots
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\FindMax[keys]{object}[node created]
\FindMin[keys]{object}[node created]
\end{tcblisting}

The optional \MontreCode{[keys]} available are:

\smallskip

\begin{itemize}
	\item \MontreCode{Method}: method, among \MontreCode{function/interpo/spline} for calculations (\MontreCode{function} by default);
	\item \MontreCode{Start}: start of the plot (\MontreCode{\textbackslash pflxmin} by default);
	\item \MontreCode{End}: end of the plot (\MontreCode{\textbackslash pflxmax} by default);
	\item \MontreCode{Step}: not in the plot if \MontreCode{function} (it is determined \textit{automatically} at the start but can be modified);
	\item \MontreCode{Coeffs}: modify the \textit{coefficients} of the spline if \MontreCode{spline};
	\item \MontreCode{Tension}: setting the \textit{tension} of the interpolation plot if \MontreCode{interpo}(\MontreCode{0.5} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=1cm,y=1cm,Xmin=-1,Xmax=5,Ymin=-1,Ymax=3]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\DefineCurve[Name=cf,Start=0.35,End=4.2,Trace]%
		<f>{0.6*cos(4.5*(x-4)+2.1)-1.2*sin(x-4)+0.1*x+0.2}
	\FindMax[Start=0.35,End=4.2]{f}[cf-max]
	\FindMax[Start=3,End=4]{f}[cf-maxlocal]
	\FindMin[Start=1,End=2]{f}[cf-minlocal]
	\MarkPts*[Color=red,Lines]{(cf-max)}
	\MarkPts*[Color=blue,Lines]{(cf-maxlocal)}
	\MarkPts*[Color=olive,Lines]{(cf-minlocal)}
	\GetXYcoord{(cf-max)}[\MyMaxX][\MyMaxY]
\end{GraphTikz}\\
The maximum is $M\approx\RoundNb{\MyMaxY}$, reached in $x\approx\RoundNb{\MyMaxX}$
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5]
	\DrawAxisGrids[Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5}
	\DefineInterpoCurve[Name=interpotest,Color=red,Trace,Tension=1]%
		{(-6,4)(-2,-2)(3,3.5)}
	\FindMin[Method=interpo,Tension=1]{(-6,4)(-2,-2)(3,3.5)}[interpo-min]
	\MarkPts*[Color=blue]{(interpo-min)}
	\GetXYcoord{(interpo-min)}[\MinInterpoX][\MinInterpoY]
\end{GraphTikz}\\
The minimum is $M\approx\RoundNb[3]{\MinInterpoY}$, reached at $x\approx\RoundNb[3]{\MinInterpoX}$
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=1.2cm,y=1.6cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=3,Ygrid=0.5,Ygrids=0.25]
	\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
	\def\LISTETEST{-6/2/0§-1/-2/0§2/1/0§3.5/0/-1}
	\DefineSplineCurve[Name=splinetest,Trace]{\LISTETEST}
	\FindMin[Method=spline]{\LISTETEST}[spline-min]
	\MarkPts*[Color=red]{(spline-min)}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Integrals (improved version)}\label{integr}

We can also work with integrals.

In this case it is preferable to highlight the domain \textbf{before} the plots, to avoid overprinting in relation to the curves/points.

\smallskip

It is possible to:

\begin{itemize}
	\item represent an integral \textbf{under} a defined curve;
	\item represent an integral \textbf{between} two curves;
	\item the integration limits can be x-coordinates and/or nodes.
\end{itemize}

\smallskip

{\small\faBomb} Given the differences in processing between formula curves, simple interpolation curves or cubic interpolation curves, the arguments and keys may differ depending on the configuration!

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawIntegral[keys]<specific options>{object1}[object2]{A}{B}
\end{tcblisting}

The optional \MontreCode{[keys]} for definition or tracing are:

\begin{itemize}
	\item \MontreCode{Colors} =: colors of the filling, in the form \MontreCode{Col} or \MontreCode{ColBorder/ColBg} (\MontreCode{gray} by default);
	\item \MontreCode{Style}: type of filling, among \MontreCode{fill}/\MontreCode{hatch} (\MontreCode{fill} by default);
	\item \MontreCode{Opacity}: opacity (\MontreCode{0.5} by default) of the filling;
	\item \MontreCode{Hatch}: style (\MontreCode{north west lines} by default) of the hatch filling;
	\item \MontreCode{Type}: type of integral among
	\begin{itemize}
		\item \MontreCode{fct} (default) for an integral under a curve defined by a formula;
		\item \MontreCode{spl} for an integral under a curve defined by a cubic spline;
		\item \MontreCode{itp} for an integral under a curve defined by interpolation;
		\item \MontreCode{fct/fct} for an integral between two curves defined by a formula;
		\item \MontreCode{fct/spl} for an integral between a curve (above) defined by a formula and a curve (below) defined by a spline cubic;
		\item etc.
	\end{itemize}
	\item \MontreCode{Step}: steps (calculated by default otherwise) for the plot;
	\item \MontreCode{Junction}: junction of segments (\MontreCode{bevel} by default);
	\item \MontreCode{Bounds}: type of terminals among:
	\begin{itemize}
		\item \MontreCode{abs} for the limits given by the abscissa;
		\item \MontreCode{nodes} for the limits given by the nodes;
		\item \MontreCode{abs/node} for the limits given by abscissa and node;
		\item \MontreCode{node/abs} for the limits given by node and abscissa;
	\end{itemize}
	\item \MontreCode{Border}: boolean (\MontreCode{true} by default) to display the side lines,%
	\item \MontreCode{SplineName}: macro (important!) of the spline generated previously for a higher version spline;
	\item \MontreCode{SplineNameB}: macro (important!) of the spline generated previously for a lower version spline;
	\item \MontreCode{InterpoName}: name (important!) of the interpolation curve generated previously, in higher version;
	\item \MontreCode{InterpoBName}: name (important!) of the interpolation curve generated previously, in lower version;
	\item \MontreCode{Tension}: Tension for the interpolation curve generated previously, in higher version;
	\item \MontreCode{TensionB}: Tension of the interpolation curve generated previously, in lower version.
\end{itemize}

\smallskip

The first required argument is the spline function or curve or list of interpolation points.

\smallskip

The next optional argument is the spline function or curve or list of interpolation points.

\smallskip

The last two mandatory arguments are the limits of the integral, given in a form consistent with the key \MontreCode{Bounds}.

\pagebreak

In the case of curves defined by \textit{points}, it is necessary to work on intervals on which the first curve is \textbf{above} the second.

It will undoubtedly be interesting to work with \textit{intersections} in this case.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.6cm,y=0.06cm,
	Xmin=0,Xmax=21,Xgrid=1,Xgrids=0.5,
	Ymin=0,Ymax=155,Ygrid=10,Ygrids=5]
	\DrawAxisGrids[Grads=false,Enlarge=2.5mm]{}{}
	\DefineCurve[Name=cf,Start=1,End=20,Color=red]<f>{80*x*exp(-0.2*x)}
	\DrawIntegral
		[Bounds=abs,Colors=blue/cyan!50]%
		{f(x)}{3}{12}
	\DrawCurve[Color=red,Start=1,End=20]{f(x)}
	\DrawAxisGrids%
		[Grid=false,Enlarge=2.5mm,Font=\small]{0,1,...,20}{0,10,...,150}
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=1.2cm,y=1.6cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=3,Ygrid=0.5,Ygrids=0.25]
	\DrawAxisGrids[Grads=false,Enlarge=2.5mm]{}{}
	\def\LISTETEST{-6/2/0§-1/-2/0§2/1/0§3.5/0/-1}
	\DefineSplineCurve[Name=splinetest]{\LISTETEST}
	\DrawIntegral[Type=spl,Style=hatch,Colors=purple]{splinetest}{-5.75}{-4.75}
	\DrawIntegral[Type=spl,Colors=blue]{splinetest}{-2}{-1}
	\DrawIntegral[Type=spl,Colors=orange]{splinetest}{1}{3}
	\DrawSplineCurve[Color=olive]{\LISTETEST}
	\DrawAxisGrids[Grid=false,Enlarge=2.5mm]
		{-7,-6,...,4}%
		{-3,-2.5,...,3}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\subsection{Tangents}\label{tgte}

The idea of this command is to draw the tangent to a previously defined curve, specifying:

\begin{itemize}
	\item the point (abscissa or node) at which we wish to work;
	\item possibly the direction (in the case of a discontinuity or a terminal);
	\item possibly the step ($h$) of the calculation;
	\item the \textit{lateral spacings} to draw the tangent.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawTangent[keys]{function or curve}{point}<line options>
\end{tcblisting}

The optional \MontreCode{[keys]} for definition or tracing are:

\begin{itemize}
	\item \MontreCode{Colors} =: colors of the plots, in the form \MontreCode{Col} or \MontreCode{ColLine/ColPoint} (\MontreCode{black} by default);
	\item \MontreCode{OffsetL} =: left horizontal spacing to start the trace (\MontreCode{1} by default);
	\item \MontreCode{OffsetR} =: left horizontal spacing to start the trace (\MontreCode{1} by default);
	\item \MontreCode{DispPt}: boolean to display the support point (\MontreCode{false} by default);
	\item \MontreCode{Spline}: boolean to specify that a spline is used (\MontreCode{false} by default);
	\item \MontreCode{h}: delta $h$ used for calculations (\MontreCode{0.01} by default);
	\item \MontreCode{Direction}: allows you to specify the \textit{direction} of the tangent, among \MontreCode{lr}/\MontreCode{l}/\MontreCode{r} (\MontreCode{lr} by default);
	\item \MontreCode{Node}: boolean to specify that a node is used (\MontreCode{false} by default).
\end{itemize}

\smallskip

The first required argument is the spline function or curve (if applicable).

\smallskip

The last mandatory argument is the work point (abscissa version or node following the key \MontreCode{Node}).

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.9cm,y=0.425cm,Xmin=4,Xmax=20,Origx=4,
	Ymin=40,Ymax=56,Ygrid=2,Ygrids=1,Origy=40]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{4,5,...,20}{40,42,...,56}
	\DefineCurve[Name=cf,Start=5,End=19,Color=red,Trace]<f>{-2*x+3+24*log(2*x)}
	\FindCounterimage[Color=teal,Name=JKL,Disp=false]{cf}{53}
	%tangent
	\DrawTangent%
		[Colors=cyan/gray,OffsetL=2.5,OffsetR=2.5,Node,DispPt]{f}{(JKL-1)}
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5]
	\DrawAxisGrids[Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5}
	\def\LISTETEST{-6/4/-0.5§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}
	\DefineSplineCurve[Name=splinetest,Trace,Color=olive]{\LISTETEST}
	\DrawTangent[Colors=red,Spline,DispPt]{splinetest}{1}
	\DrawTangent%
	[Colors=blue,Spline,OffsetL=1.5,OffsetR=1.5,DispPt]{splinetest}{-3}%
		<tkzgrpharrowlr>
	\DrawTangent[Direction=l,Colors=orange,Spline,OffsetL=1.5,DispPt]{splinetest}{3}
	\DrawTangent[Direction=r,Colors=purple,Spline,OffsetR=1.5,DispPt]{splinetest}{-6}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

%\section{Specific commands for density functions}
%
%\subsection{Normal distribution}\label{normal distribution}
%
%The idea is to provide something to work with standard deviation.
%
%\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%	%in the GraphiqueTikz environment
%	\DefineNormalDistribution[keys]<fct name>{mu}{sigma}
%	\TraceNormalDistribution[keys]{fct(x)}
%\end{tcblisting}
%
%The optional \MontreCode{[keys]} available are:
%
%\smallskip
%
%\begin{itemize}
%	\item \MontreCode{Name}: name of the plot (\MontreCode{Gaussian} by default);
%	\item \MontreCode{Trace}: boolean to trace the curve (\MontreCode{false} by default);
%	\item \MontreCode{Couleur}: color of the trace, if requested (\MontreCode{black} by default);
%	\item \MontreCode{Debut}: lower bound of the definition set (\MontreCode{\textbackslash pflxmin} by default);
%	\item \MontreCode{End}: lower bound of the definition set (\MontreCode{\textbackslash pflxmax} by default);
%	\item \MontreCode{Pas}: plot step (it is determined \textit{automatically} at the start but can be modified).
%\end{itemize}
%
%Note that the vertical axis must be adapted according to the parameters of the normal law.
%
%\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%	\begin{GraphTikz}%
%		[x=1.25cm,y=15cm,Origx=5,Xmin=5,Xmax=15,Ymin=0,Ymax=0.3,
%		Ygrid=0.1,Ygrids=0.05]
%		\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
%		\DefineNormalDistribution[Name=Gaussian]<phi>{10}{1.5}
%		\TracerIntegral
%		[Terminals=abs, Colors=blue/cyan!50]%
%		{phi(x)}{7}{13}
%		\TraceNormalLaw[Color=purple,Start=5,End=15]{phi(x)}
%	\end{GraphTikz}
%\end{tcblisting}
%
%\pagebreak
%
%\subsection{Chi-square law}\label{loikhideux}
%
%The idea is to provide something to work with normal laws.
%
%\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%	%in the GraphiqueTikz environment
%	\DefineKhiTwoLaw[keys]<fct name>{k}
%	\TraceLawKhiTwo[keys]{fct(x)}
%\end{tcblisting}
%
%The optional \MontreCode{[keys]} available are:
%
%\smallskip
%
%\begin{itemize}
%	\item \MontreCode{Name}: name of the plot (\MontreCode{Gaussian} by default);
%	\item \MontreCode{Trace}: boolean to trace the curve (\MontreCode{false} by default);
%	\item \MontreCode{Couleur}: color of the trace, if requested (\MontreCode{black} by default);
%	\item \MontreCode{Debut}: lower bound of the definition set (\MontreCode{\textbackslash pflxmin} by default);
%	\item \MontreCode{End}: lower bound of the definition set (\MontreCode{\textbackslash pflxmax} by default);
%	\item \MontreCode{Pas}: plot step (it is determined \textit{automatically} at the start but can be modified).
%\end{itemize}
%
%Note that the vertical axis must be adapted according to the parameter of the chi-square law.
%
%\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%	\begin{GraphTikz}[
%		x=1.5cm,y=7.5cm,
%		Xmin=0,Xmax=8,Xgrid=1,Xgrids=0.5,
%		Ymin=0,Ymax=0.5,Ygrid=0.1,Ygrids=0.05
%		]
%		\DrawAxisGrids[Enlarge=2.5mm]{auto}{auto}
%		\DefineKhiTwoLaw[Color=red,Start=0.25,Trace]<phiA>{1}
%		\DefineKhiTwoLaw[Color=blue,Trace]<phiB>{2}
%		\DefineLawKhiDeux[Color=orange,Trace]<phiC>{3}
%		\DefineKhiTwoLaw[Color=purple,Trace]<phiD>{4}
%		\DefineKhiTwoLaw[Color=yellow,Trace]<phiE>{5}
%		\DefineKhiTwoLaw[Color=teal,Trace]<phiF>{6}
%	\end{GraphTikz}
%\end{tcblisting}

\subsection{Linear inequality}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%within graphTike environment
\LinearInequality[keys]<function name>{expression}{symbol}
\end{tcblisting}

First argument, \textit{optional} and within \MontreCode{[...]}, gives following keys:

\begin{itemize}
	\item \MontreCode{opacity=...} (\MontreCode{0.25} by default) ;
	\item \MontreCode{color=...} (\MontreCode{black} by default) ;
	\item \MontreCode{style=...} (\MontreCode{hatch} by default) ;
	\item \MontreCode{hatch} (\MontreCode{north west lines} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[color=blue]{-3x+2}{>0}
\end{GraphTikz}
~~
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[color=pink]{-x+y+2}{<=0}
\end{GraphTikz}
~~
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[color=teal]{-x+y-4}{>0}
\end{GraphTikz}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[color=blue]{-4*y+5}{<=0}
\end{GraphTikz}
~~
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[color=pink,hatch={north east lines}]{-x-2y+2}{<=0}
\end{GraphTikz}
~~
\begin{GraphTikz}[x=0.4cm,y=0.4cm,Xmin=-5,Xmax=5,Ymin=-5,Ymax=5]
	\DrawAxisGrids[Font=\tiny]{auto}{auto}
	\LinearInequality[style=fill,color=teal]{-x-y-4}{>0}
\end{GraphTikz}
\end{tcblisting}

\pagebreak

\section{Commands specific to two-variable statistics}

\subsection{Limitations}

Given the specific features of \TikZ, we advise you not to use values that are too \textit{large} at axis level (this can cause problems with years, for example), or else you'll have to \textit{transform} axis and/or data values so that everything is displayed as it should be (also beware of regressions, calculations, etc.).

\subsection{The point scatter}\label{scatter}

In addition to commands linked to functions, it is also possible to represent double statistical series.

\smallskip

The following paragraph shows that adding a key allows you to add the linear adjustment line.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\DrawScatter[keys]{ListX}{ListY}
\end{tcblisting}

The optional \MontreCode{[key]} is:

\smallskip

\begin{itemize}
	\item \MontreCode{ColorScatter}: color of the cloud points (\MontreCode{black} by default).
\end{itemize}

\smallskip

The mandatory arguments allow you to specify:

\smallskip

\begin{itemize}
	\item the list of x;
	\item the list of y.
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.075cm,y=0.03cm,Xmin=0,Xmax=160,Xgrid=20,Xgrids=10,
	Origy=250,Ymin=250,Ymax=400,Ygrid=25,Ygrids=5]
	%window preparation
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{0,10,...,160}{250,275,...,400}
	%A cloud of dots
	\DrawScatter[Style=x,ColorScatter=red]{0,50,100,140}{275,290,315,350}
\end{GraphTikz}
\end{tcblisting}

\subsection{The regression line}\label{reglin}

The linear regression line (obtained by the least squares method) can easily be added, using the key \MontreCode{DrawLine}.

\smallskip

In this case, new keys are available:

\smallskip

\begin{itemize}
	\item \MontreCode{ColorLine}: color of the line (\MontreCode{black} by default);
	\item \MontreCode{Rounds}: precision of coefficients (\MontreCode{empty} by default);
	\item \MontreCode{Start}: initial abscissa of the plot (\MontreCode{\textbackslash pflxmin} by default);
	\item \MontreCode{End}: terminal abscissa of the plot (\MontreCode{\textbackslash pflxmax} by default);
	\item \MontreCode{Name}: name of the line, for later use (\MontreCode{reglin} by default).
\end{itemize}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=0.075cm,y=0.03cm,Xmin=0,Xmax=160,Xgrid=20,Xgrids=10,
	Origy=250,Ymin=250,Ymax=400,Ygrid=25,Ygrids=5]
	\DrawAxisGrids[Enlarge=2.5mm,Font=\small]{0,10,...,160}{250,275,...,400}
	%cloud and right
	\DrawScatter%
		[ColorScatter=red,ColorLine=brown,DrawLine]%
	{0,50,100,140}{275,290,315,350}
	%picture
	\DrawRanges[Colors=cyan/magenta,Lines]{d}{120}
	%history
	\DrawCounterimage[Style=x,Colors=blue/green!50!black,Lines]{reglin}{300}
\end{GraphTikz}
\end{tcblisting}

\subsection{Other regressions}\label{regressions}

In partnership with the \MontreCode{xint-regression} package, loaded by the package (but \textit{can be deactivated} via the \MontreCode{[noxintreg]} option), it is possible to work on other types of regression:

\begin{itemize}
	\item linear \fbox{$ax+b$};
	\item quadratic \fbox{$ax^2+bx+c$};
	\item cubic \fbox{$ax^3+bx^2+cx+d$};
	\item power \fbox{$ax^b$};
	\item exponential \fbox{$ab^x$} or \fbox{$e^{ax+b}$} or \fbox{$b e^{ax}$} or \fbox{$C + be^{ax} $};
	\item logarithmic \fbox{$a+b\ln(x)$};
	\item hyperbolic  \fbox{$a+\displaystyle\frac{b}{x}$}.
\end{itemize}

The command, similar to that of defining a curve, is:

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\DrawRegression[keys]<name fct>{type}<rounded>{listex}{listey}
\end{tcblisting}

The \MontreCode{[keys]} available are, classically:

\begin{itemize}
	\item \MontreCode{Start}: lower bound of the definition set (\MontreCode{\textbackslash pflxmin} by default);
	\item \MontreCode{End}: lower bound of the definition set (\MontreCode{\textbackslash pflxmax} by default);
	\item \MontreCode{Name}: name of the curve (important for the rest!);
	\item \MontreCode{Color}: color of the trace (\MontreCode{black} by default);
	\item \MontreCode{Step}: plot step (it is determined \textit{automatically} at the start but can be modified).
\end{itemize}

\pagebreak

The second argument, optional and between \MontreCode{<...>}, allows you to name the regression function.

The third argument, mandatory and between \MontreCode{\{...\}} allows you to choose the type of regression, among:

\begin{itemize}
	\item \MontreCode{lin}: linear \fbox{$ax+b$};
	\item \MontreCode{quad}: quadratic \fbox{$ax^2+bx+c$};
	\item \MontreCode{cub}: cubic \fbox{$ax^3+bx^2+cx+d$};
	\item \MontreCode{pow}: power \fbox{$ax^b$};
	\item \MontreCode{expab}: exponential \fbox{$ab^x$}
	\item \MontreCode{hyp}: hyperbolic \fbox{$a+\displaystyle\frac{b}{x}$};
	\item \MontreCode{log}: logarithmic \fbox{$a+b\ln(x)$};
	\item \MontreCode{exp}: exponential \fbox{$e^{ax+b}$};
	\item \MontreCode{expalt}: exponential \fbox{$be^{ax}$};
	\item \MontreCode{expoff=C}: exponential \fbox{$C + be^{ax}$}.
\end{itemize}

The fourth argument, optional and between \MontreCode{<...>}, allows you to specify the rounding(s) for the coefficients of the regression function.

The last two arguments are the lists of values of X and Y.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\def\LISTEXX{0,50,100,140}\def\LISTEYY{275,290,315,350}%
ListX:= \LISTEXX\\
ListY:= \LISTEYY

\begin{GraphTikz}
	[x=0.05cm,y=0.04cm,Xmin=0,Xmax=160,Xgrid=20,Xgrids=10,
	Origy=250,Ymin=250,Ymax=400,Ygrid=25,Ygrids=5]
	%window preparation
	\DrawAxisGrids[Enlarge=2.5mm,Font=\footnotesize]{auto}{auto}
	%A cloud of dots
	\DrawScatter[Style=o,ColorScatter=red]{\LISTEXX}{\LISTEYY}
	%adjustment expoffset
	\DrawRegression[Color=blue,Name=adjust]<adjust>{expoff=250}{\LISTEXX}{\LISTEYY}
	%holdings
	\DrawRanges[Colors=cyan/magenta,Lines]{adjust}{80}
	\DrawCounterimage[Style=x,Colors=blue/green!50!black,Lines]{adjust}{325}
\end{GraphTikz}

\xintexpoffreg[offset=250,round=3/1]{\LISTEXX}{\LISTEYY}%
We obtain $y=250+\num{\expregoffb}\text{e}^{\num{\expregoffa}x}$
\end{tcblisting}

\newpage

\section{Auxiliary commands}

\subsection{Intro}

In addition to purely \textit{graphic} commands, some auxiliary commands are available:

\begin{itemize}
	\item a to format a number with a given precision;
	\item one for working on random numbers, with constraints.
\end{itemize}

\subsection{Formatted rounding}\label{round number}

The \MontreCode{\textbackslash RoundNb} command allows you to format, using the \MontreCode{siunitx} package, a number (or a calculation), with a given precision. This can be \textit{useful} for formatting results obtained using coordinate retrieval commands, for example.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\RoundNb[precision]{xint calculation}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\RoundNb{1/3}\\
\RoundNb{16.1}\\
\RoundNb[3]{log(10)}\\
\end{tcblisting}

\subsection{Random number under constraints}\label{nbalea}

The idea of this second command is to be able to determine a random number:

\begin{itemize}
	\item integer or decimal;
	\item under constraints (between two fixed values).
\end{itemize}

This can allow, for example, to work on curves with \textit{random} points, but respecting certain constraints.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
\PickRandomNb(*)[precision (def 0)]{lower limit}{upper limit}[\macro]
\end{tcblisting}

The star version takes the constraints in strict form ($\text{lower bound} < \text{macro} < \text{upper bound}$) while the normal version takes the constraints in broad form ($\text{lower bound) } \leq \text{macro} \leq \text{upper bound}$).

\smallskip

Note that the \textit{terminals} can be existing \textit{macros}!

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%a number (2 digits after the decimal point) between 0.75 and 0.95
%a number (2 digits after the decimal point) between 0.05 and 0.25
%a number (2 decimal places) between 0.55 and \YrandMax
%a number (2 decimal places) between \YrandMin and 0.45
\PickRandomNb[2]{0.75}{0.95}[\YrandMax]%
\PickRandomNb[2]{0.05}{0.25}[\YrandMin]%
\PickRandomNb*[2]{0.55}{\YrandMax}[\YrandA]%
\PickRandomNb*[2]{\YrandMin}{0.45}[\YrandB]%
%verification
\num{\YrandMax} \& \num{\YrandMin} \& \num{\YrandA} \& \num{\YrandB}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%a number (2 digits after the decimal point) between 0.75 and 0.95
%a number (2 digits after the decimal point) between 0.05 and 0.25
%a number (2 decimal places) between 0.55 and \YrandMax
%a number (2 decimal places) between \YrandMin and 0.45
\PickRandomNb[2]{0.75}{0.95}[\YrandMax]%
\PickRandomNb[2]{0.05}{0.25}[\YrandMin]%
\PickRandomNb*[2]{0.55}{\YrandMax}[\YrandA]%
\PickRandomNb*[2]{\YrandMin}{0.45}[\YrandB]%
%verification
\num{\YrandMax} \& \num{\YrandMin} \& \num{\YrandA} \& \num{\YrandB}
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
%the curve is designed so that there are 3 antecedents
\PickRandomNb[2]{0.75}{0.95}[\YrandMax]%
\PickRandomNb[2]{0.05}{0.25}[\YrandMin]%
\PickRandomNb*[2]{0.55}{\YrandMax}[\YrandA]%
\PickRandomNb*[2]{\YrandMin}{0.45}[\YrandB]%

\begin{GraphTikz}
	[x=0.075cm,y=7.5cm,Xmin=0,Xmax=150,Xgrid=10,Xgrids=5,
	Ymin=0,Ymax=1,Ygrid=0.1,Ygrids=0.05]
	\DrawAxisGrids[Last,Enlarge=2.5mm]{auto}{auto}
	\DefineInterpoCurve[Color=red,Trace,Name=functiontest,Tension=0.75]
		{(0,\YrandA)(40,\YrandMin)(90,\YrandMax)(140,\YrandB)}
	\FindCounterimage[Disp=false,Name=ANTECED]{functiontest}{0.5}
	\DrawCounterimage[Colors=blue/teal,Lines]{functiontest}{0.5}
	\GetXcoord{(ANTECED-1)}[\Aalpha]
	\GetXcoord{(ANTECED-2)}[\Bbeta]
	\GetXcoord
	{(ANTECED-3)}[\Cgamma]
\end{GraphTikz}

The solutions of $f(x)=\num{0.5}$ are, by graphic reading:
$\begin{cases}
	\alpha \approx \RoundNb[0]{\Aalpha} \\
	\beta \approx \RoundNb[0]{\Bbeta} \\
	\gamma \approx \RoundNb[0]{\Cgamma}
\end{cases}$.
\end{tcblisting}

\subsection{Monte-Carle method}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%in the GraphiqueTikz environment
\SimulateMonteCarlo[keys]{<function>}{number of points}[\nbptsmcok][\nbptsmcko]
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5}
\begin{GraphTikz}%
	[x=10cm,y=10cm,Xmin=0,Xmax=1,Xgrid=0.1,Xgrids=0.05,
	Ymin=0,Ymax=1,Ygrid=0.1,Ygrids=0.05]
	\DrawAxisGrids[Enlarge=2.5mm,Last]{auto}{auto}
	\DefineCurve[Trace,Color=teal,Step=0.001]<f>{sqrt(1-x^2)}
	\SimulateMonteCarlo<f>{5000}
\end{GraphTikz}

There is \textcolor{blue}{\num{\nbptsmcok}} blue points,
there is \textcolor{red}{\num{\nbptsmcko}} red points.

And $\frac{\num{\nbptsmcok}}{\num{\nbptsmc}}
\approx \RoundNb[4]{\nbptsmcok/\nbptsmc}$
et $\frac{\pi}{4} \approx \RoundNb[4]{pi/4}$.
\end{tcblisting}

\pagebreak

\subsection{Some pgfplots macros}

In addition to pgfplots/axis, there's few \textit{simple} macros in order to work with \MontreCode{pgfplots/axis} environment.

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%find intersection of two [name path] objects defined
\findintersectionspgf[nodename baises]{object1}{object2}[\myt]
%global extraction of coordinates
\gextractxnodepgf{node}[\myxcoord]
\gextractynodepgf{node}[\myycoord]
\gextractxynodepgf{node}[\myxcoord][\myycoord]
%area between curves
\fillbetweencurvespgf[tikz options]{curve1}{curve2}<soft domain options>
%cubic splines
\addplotspline(*)[tikz options]<coeffs>{list of points}[\myspline]
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,listing only}
%\usepackage{alphalph}

\begin{tikzpicture}
	\begin{axis}%
		[%
		axis y line=center,axis x line=middle,                                   %axis
		axis line style={line width=0.8pt,-latex},
		x=0.33cm,y=0.55cm,xmin=1985,xmax=2030,ymin=56,ymax=70,                   %units
		grid=both,xtick distance=5,ytick distance=2,                             %gridp
		minor x tick num=4,minor y tick num=1,                                   %grids
		extra x ticks={1985},extra x tick style={grid=none},                     %origx
		extra y ticks={56},extra y tick style={grid=none},                       %origy
		x tick label style={/pgf/number format/.cd,use comma,1000 sep={}},       %year
		major tick length={2*3pt},minor tick length={1.5*3pt},                   %grads
		every tick/.style={line width=0.8pt},enlargelimits=false,                %style
		enlarge x limits={abs=2.5mm,upper},enlarge y limits={abs=2.5mm,upper},   %énlarge
		]
		%spline + y=66
		\addplot[name path global=eqtest,mark=none,red,line width=1.05pt,domain=1985:2030] {66} ;
		\def\LISTETEST{1985/60/0§1995/68/0§2015/58/0§2025/69/0§2030/62/-2}
		\addplotspline*[line width=1.05pt,violet,name path global=splinecubtest]{\LISTETEST}[\monsplineviolet]
		%equation f(x)=66
		\findintersectionspgf[MonItsc]{eqtest}{splinecubtest}
		%extraction of coordinates
		\gextractxnodepgf{(MonItsc-1)}[\xMonItscA]
		\gextractxnodepgf{(MonItsc-2)}[\xMonItscB]
		\gextractxnodepgf{(MonItsc-3)}[\xMonItscC]
		\gextractxnodepgf{(MonItsc-4)}[\xMonItscD]
		%vizualisation
		\xintFor* #1 in {\xintSeq{1}{4}}\do{%
			\draw[line width=0.9pt,densely dashed,olive,->,>=latex] (MonItsc-#1) -- (\csname xMonItsc\AlphAlph{#1}\endcsname,56) ;
			\filldraw[olive] (MonItsc-#1) circle[radius=1.75pt] ;
		}
		%area
		\path [name path=xaxis] (1985,56) -- (2030,56);
		\fillbetweencurvespgf{splinecubtest}{xaxis}<domain={\xMonItscB:\xMonItscA}>
		\fillbetweencurvespgf{splinecubtest}{xaxis}<domain={\xMonItscD:\xMonItscC}>
	\end{axis}
\end{tikzpicture}

Solutions of  $f(x)=66$ are \RoundNb[0]{\xMonItscA} \&\ \RoundNb[0]{\xMonItscB} \&\ \RoundNb[0]{\xMonItscC} \&\ \RoundNb[0]{\xMonItscD}.
\end{tcblisting}

\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5,text only}
\begin{tikzpicture}
	\begin{axis}%
		[%
		axis y line=center,axis x line=middle,                                   %axis
		axis line style={line width=0.8pt,-latex},
		x=0.33cm,y=0.55cm,xmin=1985,xmax=2030,ymin=56,ymax=70,                   %units
		grid=both,xtick distance=5,ytick distance=2,                             %gridp
		minor x tick num=4,minor y tick num=1,                                   %grids
		extra x ticks={1985},extra x tick style={grid=none},                     %origx
		extra y ticks={56},extra y tick style={grid=none},                       %origy
		x tick label style={/pgf/number format/.cd,use comma,1000 sep={}},       %year
		major tick length={2*3pt},minor tick length={1.5*3pt},                   %grads
		every tick/.style={line width=0.8pt},enlargelimits=false,                %style
		enlarge x limits={abs=2.5mm,upper},enlarge y limits={abs=2.5mm,upper},   %énlarge
		]
		%spline + y=66
		\addplot[name path global=eqtest,mark=none,red,line width=1.05pt,domain=1985:2030] {66} ;
		\def\LISTETEST{1985/60/0§1995/68/0§2015/58/0§2025/69/0§2030/62/-2}
		\addplotspline*[line width=1.05pt,violet,name path global=splinecubtest]{\LISTETEST}[\monsplineviolet]
		%equation f(x)=66
		\findintersectionspgf[MonItsc]{eqtest}{splinecubtest}
		%extraction of coordinates
		\gextractxnodepgf{(MonItsc-1)}[\xMonItscA]
		\gextractxnodepgf{(MonItsc-2)}[\xMonItscB]
		\gextractxnodepgf{(MonItsc-3)}[\xMonItscC]
		\gextractxnodepgf{(MonItsc-4)}[\xMonItscD]
		%vizualisation
		\xintFor* #1 in {\xintSeq{1}{4}}\do{%
			\draw[line width=0.9pt,densely dashed,olive,->,>=latex] (MonItsc-#1) -- (\csname xMonItsc\AlphAlph{#1}\endcsname,56) ;
			\filldraw[olive] (MonItsc-#1) circle[radius=1.75pt] ;
		}
		%area
		\path [name path=xaxis] (1985,56) -- (2030,56);
		\fillbetweencurvespgf{splinecubtest}{xaxis}<domain={\xMonItscB:\xMonItscA}>
		\fillbetweencurvespgf{splinecubtest}{xaxis}<domain={\xMonItscD:\xMonItscC}>
	\end{axis}
\end{tikzpicture}

Solutions of  $f(x)=66$ are \RoundNb[0]{\xMonItscA} \&\ \RoundNb[0]{\xMonItscB} \&\ \RoundNb[0]{\xMonItscC} \&\ \RoundNb[0]{\xMonItscD}.
\end{tcblisting}

\section{History}

\begin{quote}
\begin{verbatim}
0.30f: Bugfix + new commands (stats in [fr] version)
0.30e: New commands (experimental in [fr] version)
0.30d: New commands (experimental in [fr] version)
0.30c: New version of code, with [en/fr] separate versions + macros for calculate
------ New commands (experimental in [fr] version)
0.30b: New commands (experimental in [fr] version)
0.30a: Nodes for windows and axis
0.2.9: New keys for french version (work in progress)
0.2.7: Ability to specify dimensions for environment (test)
0.2.6: Linear inequality (work in progress)
0.2.5: Lagrange interpolation ([french] for the moment) + enhancements
0.2.4: Bugfix with [fr] version
0.2.3: Bugfix with a length
0.2.2: Bugfixes
0.2.0: [Alt] key for Hermite spline + few pgfplots macros
0.1.9: Bugfix
0.1.8: New commands [in french doc] (binomial, cabweb,\ldots)
0.1.6: Vertical asymptote + [in french doc] commands for integrals
0.1.5: Initial version [en]
\end{verbatim}
\end{quote}

\end{document}